Book · January 994 citations 110 reads 2,264 authors

partly under his influence. Presumably, this makes him one of the few scien-
tists who can constructively criticize nearly all the chapters in this book.
Without doubt, one criticism will be the almost total omission of explicit
discussions on theories of mathematics education. However, the very con-
cept of this book is to show just how these theories may be applied.
ACKNOWLEDGEMENTS
The concept of this book was born in early summer 1992. The chapters were
divided among the editors and contacts were initiated with possible authors
of specific articles in summer and autumn 1992. In contrast to experiences
with other edited books, the vast majority of answers to our call for papers
were positive. Many authors named their friendship to Hans-Georg Steiner
and their appreciation of his and the IDM's work as decisive motives for
their decision to collaborate, even if there were serious difficulties in joining
the book project due to other commitments. We are very grateful to all our
authors and hereby thank them for their excellent work.
All the authors provided abstracts of their papers, which were reviewed
by the chapter editors and exchanged between authors of the same chapter.
The full papers reached the editors in spring and early summer 1993 and
were reviewed by the editors. The articles were revised or partly rewritten
till the end of June, 1993.
We want to thank Herta Ritsche, secretary at the IDM, who was respon-
sible for producing the camera-ready copies. She was at the center of the
production of the book. She carefully managed the many successive ver-
sions of the papers and coordinated the editorial work.
We want to thank Jonathan Harrow and Günter Seib for translating some
of the chapters. We are indebted to Jonathan Harrow not just for his perfect
7

---

PREFACE
language checks and stylistic polishing of most of the papers, including
some papers by English native speakers. His professional approach to the
final formal editing and his remarks and suggestions on many formulations
helped to clarify many texts and has made them more easily accessible for
the reader. Without such generous and dedicated help, this book would not
have been possible. However, the editors are fully responsible for any re-
maining printing errors and mistakes due to the editing process.
We wish the IDM and Hans-Georg Steiner a good and productive future
in their continued efforts to promote the didactics of mathematics as a scien-
tific discipline!
Rolf Biehler
Roland W. Scholz
Rudolf Sträßer
Bernard Winkelmann
8

---

CHAPTER
1
PREPARING MATHEMATICS FOR STUDENTS
edited and introduced
by
Bernard Winkelmann
Bielefeld
For many didacticians of mathematics, reflections on and improvements in
the process of the curriculum development and implementation of mathe-
matics teaching are both the starting point and motivating goal of their re-
search. They serve as a main goal of research in mathematics teaching and
learning and as a bridge between various social groups engaged in mathe-
matics education such as teachers, parents, employers, and educationalists.
The process of preparing mathematics for students can be described from
different viewpoints and with different theoretical frameworks in mind.
Mogens Niss (this volume) uses a concise formulation when he names the
solving of the following problems as necessary actions in this process:
1. The problem of justification. Why should some specific part of mathe-
matics (considered in a broad sense) be taught to a specific group of stu-
dents?
2. The problem of possibility. Given the mental abilities of the group of
students in question, can the mathematical subject be taught, and, if so,
how?
R. Biehler, R. W. Scholz, R. Sträßer, B. Winkelmann (Eds.),